Solution 2.9.5.5 Applying the Laplace transform yields s 2 Y (s);sy(0);y [1] (0)+ 4[sY (s);y(0)];3Y (s)=0: Rearranging yields (s 2 +4s;3)Y (s)=sy(0)+ 4y(0)+ y [1] (0);; or Y (s)= sy(0)+ 4y(0)+ y [1] (0) [s +(2; p 7)][s +(2+ p 7) For the given initial conditions we then have Y (s) = 8(s +4) [s +(2; p 7)][s+(2+ p 7)] = A s +(2; p 7) + B s +(2+ p 7) : A = [s +(2; p 7)]Y (s) s=;2+ p 7 = " 8(s +4) [s +(2+ p 7)] # s=;2+ p 7 = 7:0237 B = [s +(2+ p 7)]Y (s) s=;2; p 7 = " 8(s +4) [s +(2; p 7)] # s=;2; p 7 = 0:9763 y(t) = [7:0237e (;2+ p 7)t ;0:9762e (;2; p 7)t ]1(t) = [7:0237e 0:6458t ;0:9762e ;4:6458t ]1(t) 1